CBSE Class 12 Mathematics 2026 Main Paper 65/4/1 · Q232 Marksmonotonicity
CBSE Class 12 Mathematics 2026 Main Paper 65/4/1 · Question 23 (Applications Of Derivatives)
Where is f(x)=xˣ increasing on x>0?
✅ Step-by-Step Solution
Final Answer: From 1/e onward.
- Use ln f=x ln x to obtain f′=xˣ(1+ln x).
- The derivative is positive for x>1/e and negative below it.
- Thus the increasing interval is [1/e,∞), with positive derivative on its interior.
📋 CBSE Stepwise Marking Scheme
- [0.5 marks] Use ln f=x ln x to obtain f′=xˣ(1+ln x).
- [1 mark] The derivative is positive for x>1/e and negative below it.
- [0.5 marks] Thus the increasing interval is [1/e,∞), with positive derivative on its interior.
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